Numerical simulation of unsteady flow in hydraulic turbomachines

Turbines and pumps dealing with incompressible flow are examples of hydraulic turbomachines. In most cases the flow is highly turbulent and time-dependent, caused by the rotation of the impeller in a stationary casing. The geometry, with doubly curved surfaces, adds even more to the complexity. It all leads to a flow which is difficult to model. Yet, to optimize turbomachines it is necessary to analyze the flow in detail. Flow simulations using Computational Fluid Dynamics (CFD) can be a very helpful tool. The software solves the discretized partial differential equations for mass and momentum conservation on a grid that covers the flow domain. Two basic discretization schemes can be distinguished: collocated and staggered. When a collocated scheme is used, the solution suffers from odd-even decoupling. In practice this is suppressed with artificial measures which either decrease the accuracy of the simulation or increase the calculation time for an unsteady incompressible flow. Using a staggered scheme, accurate discretization is more difficult, but odd-even decoupling is avoided. In this thesis a CFD code is developed which is based on a staggered, blockstructured grid scheme. It is suited for the calculation of time-dependent fluid motion in turbomachines. The CFD code, named DEFT, is originally developed by the group ofWesseling at Delft University of Technology. The first extension in the current work was an interpolation procedure implemented to handle non-matching grids for more flexibility in grid generation. Furthermore, a sliding interface to connect the rotating grid in the impeller and the stationary grid was developed. Coriolis and centrifugal forces for calculations in the rotating frame of reference, were mplemented in two ways: using a conservative formulation and using source terms. An adaptation of the pressure equation proved necessary to reduce calculation time for computations involving a sliding interface. Although the conceptual ideas behind these extensions are applicable in 3D, they have been implemented in 2D and verified with the simulation of a number of relatively simple flows. DeFT was validated with the simulation of the flow through a cascade of blades which is a model of an axial-flow pump. The blade surface pressure and the total force on the blade are calculated. There is good agreement between values calculated with DeFT, Fluent, values from experiments, and other CFD calculations obtained from literature. The flow through a centrifugal pump with a vaned diffusor is simulated using the staggered discretization in DeFT and the collocated discretization in Fluent. The calculated time-averaged pressure and velocity along the pitch of a rotor channel show good correspondence. The agreement with results from experiments and other CFD calculations obtained from literature is more qualitative. The calculation time needed by DeFT and Fluent is approximately equal, despite the use of a large number of blocks in DeFT and its lack of a convergence enhancing multi-grid method which is used by Fluent

Remote sensing for three-dimensional modelling of hydromorphology

Successful management of rivers requires an understanding of the fluvial processes that govern them. This, in turn cannot be achieved without a means of quantifying their geomorphology and hydrology and the spatio-temporal interactions between them, that is, their hydromorphology. For a long time, it has been laborious and time-consuming to measure river topography, especially in the submerged part of the channel. The measurement of the flow field has been challenging as well, and hence, such measurements have long been sparse in natural environments. Technological advancements in the field of remote sensing in the recent years have opened up new possibilities for capturing synoptic information on river environments. This thesis presents new developments in fluvial remote sensing of both topography and water flow. A set of close-range remote sensing methods is employed to eventually construct a high-resolution unified empirical hydromorphological model, that is, river channel and floodplain topography and three-dimensional areal flow field. Empirical as well as hydraulic theory-based optical remote sensing methods are tested and evaluated using normal colour aerial photographs and sonar calibration and reference measurements on a rocky-bed sub-Arctic river. The empirical optical bathymetry model is developed further by the introduction of a deep-water radiance parameter estimation algorithm that extends the field of application of the model to shallow streams. The effect of this parameter on the model is also assessed in a study of a sandy-bed sub-Arctic river using close-range high-resolution aerial photography, presenting one of the first examples of fluvial bathymetry modelling from unmanned aerial vehicles (UAV). Further close-range remote sensing methods are added to complete the topography integrating the river bed with the floodplain to create a seamless high-resolution topography. Boat- cart- and backpack-based mobile laser scanning (MLS) are used to measure the topography of the dry part of the channel at a high resolution and accuracy. Multitemporal MLS is evaluated along with UAV-based photogrammetry against terrestrial laser scanning reference data and merged with UAV-based bathymetry to create a two-year series of seamless digital terrain models. These allow the evaluation of the methodology for conducting high-resolution change analysis of the entire channel. The remote sensing based model of hydromorphology is completed by a new methodology for mapping the flow field in 3D. An acoustic Doppler current profiler (ADCP) is deployed on a remote-controlled boat with a survey-grade global navigation satellite system (GNSS) receiver, allowing the positioning of the areally sampled 3D flow vectors in 3D space as a point cloud and its interpolation into a 3D matrix allows a quantitative volumetric flow analysis. Multitemporal areal 3D flow field data show the evolution of the flow field during a snow-melt flood event. The combination of the underwater and dry topography with the flow field yields a compete model of river hydromorphology at the reach scale.Jokien onnistunut hallinta edellyttää virtavesien prosessien ymmärtämistä. Tämä ei ole mahdollista ilman jokien geomorfologian ja hydrologian kvantifiointia sekä niiden spatiotemporaalisten suhteiden tutkimista, eli jokien hydromorfologiaa. Joen topografian mittaaminen, varsinkin uoman vedenalaisen osalle on pitkään ollut työlästä ja aikaa vievää. Virtauskentän kattava mittaaminen on myös ollut haastavaa, sillä seurauksella, että niitä on tehty harvakseltaan luonnollisessa ympäristössä. Viimeaikainen teknologinen kehitys kaukokartoituksessa on mahdollistanut synoptisen tiedon mittaamisen jokiympäristöissä. Tässä väitöstutkimuksessa on kehitetty virtavesien kaukokartoitusta sekä jokien topografian että virtausmittauksen alalla. Useita eri lähikaukokartoitusmenetelmiä yhdistämällä on tehty korkean resoluution yhtenäinen empiirinen malli joen hydromorfologiasta, eli joen uoman ja tulvatasangon topografiasta ja kolmiulotteisesta virtaamakentästä. Empiriaan ja hydrauliseen teoriaan perustuvat optisen kaukokartoituksen menetelmiä testattiin ja arvioitiin käyttämällä normaaliväri-ilmakuvia, kaikuluotain kalibrointia ja referenssimittauksia kivipohjaisessa subarktisessa joessa. Empiiristä optista syvyysmallia kehitettiin edelleen lisäämällä syvän veden säteilyparametrin arviointialgoritmi, joka mahdollisti mallin käytön myös matalavetisissä jokiuomissa. Parametrin vaikutus malliin arvioitiin korkean resoluution matalailmakuvista hiekkapohjaisessa subarktisessa joessa yhdessä ensimmäisistä syvyysmalleista, joka on tehty käyttäen kauko-ohjattua minihelikopteria (eng.UAV, Unmanned Aerial Vehicle). Lähietäisyyden kaukokartoitusmenetelmiä käytettiin edelleen topografisen mallin täydentämiseen, integroimalla joen uoma ja tulvatasanko yhtenäiseksi korkean resoluution topografiaksi. Mobiilia laserkeilausta käytettiin vedenpinnan yläpuolisen osan topografian mittaamiseen korkealla resoluutiolla vene- kärry- ja reppupohjaisten kartoitusalustojen avulla. Monen ajankohdan mobiilin laserkeilauksen ja UAVfotogrammetrian tarkkuutta arvioitiin maalaserikeilausaineiston avulla. Laserkeilattu ja fotogrammetrinen aineisto yhdistettiin, jolloin saatiin kahden vuoden ajalta saumaton digitaalinen maastomalli. Mallin avulla oli mahdollista arvioida koko joen uoman korkean resoluution muutosanalyysin metodologiaa. Kaukokartoitukseen perustuvaa hydromorfologista mallia täydennettiin uniikilla virtauskentän kolmiulotteisella kartoitusaineistolla. Kauko-ohjattavaan veneeseen asennettu akustinen virtausmittauslaite yhdessä tarkan satelliittipaikannusjärjestelmän kanssa mahdollistivat alueellisesti valikoitujen kolmiulotteisten virtausvektoreiden sijainnin määrittämisen kolmiulotteisessa avaruudessa pistepilvenä. Tämän aineiston kolmiulotteinen interpolaatio matriisiksi mahdollisti edelleen volymetrisen virtausanalyysin. Monen ajankohdan alueellinen kolmiulotteinen virtauskenttä osoitti virtausolosuhteiden evoluution kevättulvassa. Vedenalaisen ja kuivan maan topografia yhdessä jokiuoman virtauskenttien kanssa muodosti kattavan mallin joen hydromorfologiasta.Siirretty Doriast

Hydrological post-processing based on approximate Bayesian computation (ABC)

[EN] This study introduces a method to quantify the conditional predictive uncertainty in hydrological post-processing contexts when it is cumbersome to calculate the likelihood (intractable likelihood). Sometimes, it can be difficult to calculate the likelihood itself in hydrological modelling, specially working with complex models or with ungauged catchments. Therefore, we propose the ABC post-processor that exchanges the requirement of calculating the likelihood function by the use of some sufficient summary statistics and synthetic datasets. The aim is to show that the conditional predictive distribution is qualitatively similar produced by the exact predictive (MCMC post-processor) or the approximate predictive (ABC post-processor). We also use MCMC post-processor as a benchmark to make results more comparable with the proposed method. We test the ABC post-processor in two scenarios: (1) the Aipe catchment with tropical climate and a spatially-lumped hydrological model (Colombia) and (2) the Oria catchment with oceanic climate and a spatially-distributed hydrological model (Spain). The main finding of the study is that the approximate (ABC post-processor) conditional predictive uncertainty is almost equivalent to the exact predictive (MCMC post-processor) in both scenarios.This study was partially supported by the Departamento del Huila Scholarship Program No. 677 (Colombia) and Colciencias, by the Spanish Research Project TETIS-MED (ref. CGL2014-58127-C3-3-R) and TETIS-CHANGE (ref.RTI2018-093717-B-I00). Also, G. Adelfio's research has been supported by the national grant of the Italian Ministry of Education University and Research (MIUR) for the PRIN-2015 program, "Complex space-time modelling and functional analysis for probabilistic forecast of seismic events'. 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Medical robots with potential applications in participatory and opportunistic remote sensing: A review

Among numerous applications of medical robotics, this paper concentrates on the design, optimal use and maintenance of the related technologies in the context of healthcare, rehabilitation and assistive robotics, and provides a comprehensive review of the latest advancements in the foregoing field of science and technology, while extensively dealing with the possible applications of participatory and opportunistic mobile sensing in the aforementioned domains. The main motivation for the latter choice is the variety of such applications in the settings having partial contributions to functionalities such as artery, radiosurgery, neurosurgery and vascular intervention. From a broad perspective, the aforementioned applications can be realized via various strategies and devices benefiting from detachable drives, intelligent robots, human-centric sensing and computing, miniature and micro-robots. Throughout the paper tens of subjects, including sensor-fusion, kinematic, dynamic and 3D tissue models are discussed based on the existing literature on the state-of-the-art technologies. In addition, from a managerial perspective, topics such as safety monitoring, security, privacy and evolutionary optimization of the operational efficiency are reviewed

Congiungere la modellazione dei movimenti di massa alla realtà

I flussi di massa sono pericoli naturali di tipo gravitativo tipici delle zone montane che causano ogni anno perdite economiche e vittime. I modelli numerici sono strumenti per prevedere la propagazione di potenziali eventi di flussi di massa su una determinata topografia, ma questi richiedono diversi input. Gli input e i processi che sostanzialmente influenzano i risultati dei modelli sono rappresentati dalla dal volume, dalle condizioni di innesco e dalle interazioni topografia – flusso di massa. Pertanto, l'obiettivo principale della tesi è quello di migliorare la quantificazione del volume coinvolto in un evento di flusso di massa e di aumentare la rappresentazione dell’interazione tra il flusso e la topografia. Quindi, sono stati studiati due tipi di flussi di massa: debris flow e valanghe di neve. Per quanto riguarda i debris flow, la tesi vuole migliorare l'affidabilità dei modelli analizzando l'aumento del volume del flusso attraverso l'erosione del letto del canale e il collasso di strutture di mitigazione. Per le valanghe di neve, lo studio ha come obbiettivo quello di migliorare l'identificazione delle possibili aree di distacco. La tesi è strutturata come una raccolta di articoli dei quali tre sono stati pubblicati e uno è in fase di revisione. Il primo articolo ha migliorato la rappresentazione dei fenomeni erosivi nei modelli numerici grazie ai dati di un evento di debris flow avvenuto nel bacino del rio Gere (Veneto, IT). Una funzione basata sui valori di pendenza è stata definita per calcolare il coefficiente di erosione, successivamente utilizzato per riprodurre l’erosione osservata nel canale. I risultati sono utili per migliorare l'accuratezza di futuri scenari da debris flow per i quali l'erosione è un importante processo nella dinamica del flusso. Il secondo studio ha definito una procedura per simulare l'effetto del collasso delle briglie di consolidamento in un evento di debris flow. La metodologia è stata sviluppata nel rio Rotian (Trentino, IT), dove un evento di pioggia estrema ha innescato un debris flow che ha provocato il collasso di una serie di 15 briglie. La metodologia sviluppata può essere direttamente applicata per mappare il rischio residuo dei canali da debris flow in cui siano presenti opere o dove la mancanza di manutenzione delle misure di mitigazione può diminuire la loro stabilità. Il terzo progetto riguarda lo studio della rugosità del terreno. Sette algoritmi di calcolo della rugosità sono stati testati in due aree studio al fine di identificare quale algoritmo possa rappresentare nel modo più appropriato le tipologie del terreno che interagiscono con i fenomeni di massa. I risultati hanno mostrato che il miglior algoritmo è risultato il vector ruggedness e che l’utilizzo di una risoluzione maggiore non ha migliorato le performance. Il quarto progetto ha analizzato la capacità di protezione delle foreste colpite da tempeste di vento. Due nuovi algoritmi per valutare le caratteristiche degli alberi abbattuti sono stati sviluppati. I risultati hanno evidenziato che il momento di protezione minimo delle foreste contro le valanghe di neve è dopo 10 anni l'evento di tempesta. Inoltre, gli algoritmi possono essere applicati direttamente su scala regionale per la gestione e il monitoraggio delle aree forestali colpite da tempeste. I diversi studi hanno analizzato i processi di erosione, l'effetto del collasso di briglie e l'identificazione di potenziali aree di innesco. I risultati dei quattro progetti hanno risposto ai corrispondenti obbiettivi, migliorando la comprensione dei flussi di massa e quindi la previsione di eventi futuri. Inoltre, i progetti forniscono importanti risultati metodologici e nuovi metodi sono stati sviluppati e testati al fine di migliorare la stima del volume dei flussi di massa. Tali metodi sono inoltre applicabili al di fuori delle aree di studio prese in esame, dando supporto a diversi stakeholder nella gestione dei rischi naturali.Mass flows are gravitational natural hazards typical of mountain areas causing economic losses and fatalities every year. Numerical models are a way to predict the propagation of potential mass flow events over a certain topography. To appropriately reproduce future events, models required different inputs. Inputs and processes consistently affecting the outcomes of mass flow models regard the released volume, the triggering conditions and the interaction with the topography and the features on the ground once the flow is in motion. Therefore, the main objective of the thesis is to improve the quantification of the input volume and to improve the implementation of processes of interaction with the basal topography. In this context, the focus has been placed on two types of mass flows: debris flows and snow avalanches. Regarding debris flows, the study aims to improve the reliability of models to capture the increase in flow volume through channel bed erosion and mitigation structure collapse. For snow avalanches, the study wants to improve the identification of possible avalanche release areas taking into account the role of different types of vegetation structures. The thesis was structured as a collection of articles of which three have been published and one is currently under review. The first paper investigated the improvement of debris flow erosion in computational models thanks to data of a severe event occurred in the Gere catchment (Veneto, IT). A function based on a smoothed terrain slope map was calibrated to derive the erosion coefficient, successively used to reproduce the observed erosion process occurred in the channel. Results can improve the reliability of future scenarios related to debris flows for which bed erosion plays an important role in volume increase. The second study defined a procedure to simulate the effect of check dam collapse in a debris flow event. The methodology was developed in the rio Rotian (Trentino, IT) where an extreme rainfall event triggered a debris flow that collapsed a series of 15 check dams. The adopted methodology can be straight applied to map the residual risk of mountain channels or where the lack of maintenance may decrease torrent countermeasure stability. The third project involves the study of terrain roughness. We tested seven algorithms computing terrain roughness in two study areas with the aim to identify which roughness algorithm can represent in the most appropriate way the features on the ground interacting with natural hazards. Outcomes showed that the best algorithm resulted the vector ruggedness and that the increase in data resolution did not improve the classification performance. Results can improve the reliability of mass flow propagation models over natural areas. The fourth project analysed the protection capacity of forests affected by windstorms. We developed and tested two algorithms to assess the characteristics of abated trees. Results assessed that the time of minimum level of forest protection against snow avalanches in 10 years after the storm event. The developed algorithms can be straight applied at regional scale to monitor and improve the management of windthrow areas. The projects investigated entrainment processes, effect of mitigation structure failures and the identification of potential triggering areas. Outcomes of the four projects filled the respective gaps of knowledge, improving the understanding of mass flows and then the prediction of future events. Furthermore, the projects have strong methodological outcomes and new methods to improve the volume estimation of mass flows have been developed and tested. Such methods are further applicable outside of the study areas, supporting different stakeholders in the management of natural hazards of mountain areas

Congiungere la modellazione dei movimenti di massa alla realtà

I flussi di massa sono pericoli naturali di tipo gravitativo tipici delle zone montane che causano ogni anno perdite economiche e vittime. I modelli numerici sono strumenti per prevedere la propagazione di potenziali eventi di flussi di massa su una determinata topografia, ma questi richiedono diversi input. Gli input e i processi che sostanzialmente influenzano i risultati dei modelli sono rappresentati dalla dal volume, dalle condizioni di innesco e dalle interazioni topografia – flusso di massa. Pertanto, l'obiettivo principale della tesi è quello di migliorare la quantificazione del volume coinvolto in un evento di flusso di massa e di aumentare la rappresentazione dell’interazione tra il flusso e la topografia. Quindi, sono stati studiati due tipi di flussi di massa: debris flow e valanghe di neve. Per quanto riguarda i debris flow, la tesi vuole migliorare l'affidabilità dei modelli analizzando l'aumento del volume del flusso attraverso l'erosione del letto del canale e il collasso di strutture di mitigazione. Per le valanghe di neve, lo studio ha come obbiettivo quello di migliorare l'identificazione delle possibili aree di distacco. La tesi è strutturata come una raccolta di articoli dei quali tre sono stati pubblicati e uno è in fase di revisione. Il primo articolo ha migliorato la rappresentazione dei fenomeni erosivi nei modelli numerici grazie ai dati di un evento di debris flow avvenuto nel bacino del rio Gere (Veneto, IT). Una funzione basata sui valori di pendenza è stata definita per calcolare il coefficiente di erosione, successivamente utilizzato per riprodurre l’erosione osservata nel canale. I risultati sono utili per migliorare l'accuratezza di futuri scenari da debris flow per i quali l'erosione è un importante processo nella dinamica del flusso. Il secondo studio ha definito una procedura per simulare l'effetto del collasso delle briglie di consolidamento in un evento di debris flow. La metodologia è stata sviluppata nel rio Rotian (Trentino, IT), dove un evento di pioggia estrema ha innescato un debris flow che ha provocato il collasso di una serie di 15 briglie. La metodologia sviluppata può essere direttamente applicata per mappare il rischio residuo dei canali da debris flow in cui siano presenti opere o dove la mancanza di manutenzione delle misure di mitigazione può diminuire la loro stabilità. Il terzo progetto riguarda lo studio della rugosità del terreno. Sette algoritmi di calcolo della rugosità sono stati testati in due aree studio al fine di identificare quale algoritmo possa rappresentare nel modo più appropriato le tipologie del terreno che interagiscono con i fenomeni di massa. I risultati hanno mostrato che il miglior algoritmo è risultato il vector ruggedness e che l’utilizzo di una risoluzione maggiore non ha migliorato le performance. Il quarto progetto ha analizzato la capacità di protezione delle foreste colpite da tempeste di vento. Due nuovi algoritmi per valutare le caratteristiche degli alberi abbattuti sono stati sviluppati. I risultati hanno evidenziato che il momento di protezione minimo delle foreste contro le valanghe di neve è dopo 10 anni l'evento di tempesta. Inoltre, gli algoritmi possono essere applicati direttamente su scala regionale per la gestione e il monitoraggio delle aree forestali colpite da tempeste. I diversi studi hanno analizzato i processi di erosione, l'effetto del collasso di briglie e l'identificazione di potenziali aree di innesco. I risultati dei quattro progetti hanno risposto ai corrispondenti obbiettivi, migliorando la comprensione dei flussi di massa e quindi la previsione di eventi futuri. Inoltre, i progetti forniscono importanti risultati metodologici e nuovi metodi sono stati sviluppati e testati al fine di migliorare la stima del volume dei flussi di massa. Tali metodi sono inoltre applicabili al di fuori delle aree di studio prese in esame, dando supporto a diversi stakeholder nella gestione dei rischi naturali.Mass flows are gravitational natural hazards typical of mountain areas causing economic losses and fatalities every year. Numerical models are a way to predict the propagation of potential mass flow events over a certain topography. To appropriately reproduce future events, models required different inputs. Inputs and processes consistently affecting the outcomes of mass flow models regard the released volume, the triggering conditions and the interaction with the topography and the features on the ground once the flow is in motion. Therefore, the main objective of the thesis is to improve the quantification of the input volume and to improve the implementation of processes of interaction with the basal topography. In this context, the focus has been placed on two types of mass flows: debris flows and snow avalanches. Regarding debris flows, the study aims to improve the reliability of models to capture the increase in flow volume through channel bed erosion and mitigation structure collapse. For snow avalanches, the study wants to improve the identification of possible avalanche release areas taking into account the role of different types of vegetation structures. The thesis was structured as a collection of articles of which three have been published and one is currently under review. The first paper investigated the improvement of debris flow erosion in computational models thanks to data of a severe event occurred in the Gere catchment (Veneto, IT). A function based on a smoothed terrain slope map was calibrated to derive the erosion coefficient, successively used to reproduce the observed erosion process occurred in the channel. Results can improve the reliability of future scenarios related to debris flows for which bed erosion plays an important role in volume increase. The second study defined a procedure to simulate the effect of check dam collapse in a debris flow event. The methodology was developed in the rio Rotian (Trentino, IT) where an extreme rainfall event triggered a debris flow that collapsed a series of 15 check dams. The adopted methodology can be straight applied to map the residual risk of mountain channels or where the lack of maintenance may decrease torrent countermeasure stability. The third project involves the study of terrain roughness. We tested seven algorithms computing terrain roughness in two study areas with the aim to identify which roughness algorithm can represent in the most appropriate way the features on the ground interacting with natural hazards. Outcomes showed that the best algorithm resulted the vector ruggedness and that the increase in data resolution did not improve the classification performance. Results can improve the reliability of mass flow propagation models over natural areas. The fourth project analysed the protection capacity of forests affected by windstorms. We developed and tested two algorithms to assess the characteristics of abated trees. Results assessed that the time of minimum level of forest protection against snow avalanches in 10 years after the storm event. The developed algorithms can be straight applied at regional scale to monitor and improve the management of windthrow areas. The projects investigated entrainment processes, effect of mitigation structure failures and the identification of potential triggering areas. Outcomes of the four projects filled the respective gaps of knowledge, improving the understanding of mass flows and then the prediction of future events. Furthermore, the projects have strong methodological outcomes and new methods to improve the volume estimation of mass flows have been developed and tested. Such methods are further applicable outside of the study areas, supporting different stakeholders in the management of natural hazards of mountain areas

Navigation algorithm for INS/GPS Data Fusion

Diplomová práce se zabývá návrhem algoritmu rozšířeného Kalmanova filtru, který integruje data z inerciálního navigačního systému (INS) a globálního polohovacího systému (GPS). Součástí algoritmu je i samotná mechanizace INS, určující na základě dat z akcelerometrů a gyroskopů údaje o rychlosti, zeměpisné pozici a polohových úhlech letadla. Vzhledem k rychlému nárůstu chybovosti INS je výstup korigován hodnotami rychlosti a pozice získané z GPS. Výsledný algoritmus je implementován v prostředí Simulink. Součástí práce je odvození jednotlivých stavových matic rozšířeného Kalmanova filtru.This diploma thesis deals with Extended Kalman Filter algorithm fusing data from inertial navigation system (INS) and Global Positioning System (GPS). The part of the developed algorithm is a mechanization of INS which processes data from accelerometers and gyroscopes to provide velocity, position and attitude angles. Due to rapid increase of INS output errors, the EKF is used to correct INS outputs by velocity and position from GPS. The final algorithm is developed in Simulink environment. This thesis includes derivation of EKF state matrices.